Simple solutions: Combine military needs and immigration reform

I don't have all the answers, but no one human does. So here's the plan: Allow unlimited immigration to the United States with the caveat that all males and females immediately enlist in the military, branch of their choice, as a price for admission. Once they serve a four year contract, which automatically includes overseas deployment, they get their citizenship.
That's it. Simple, but there are these inherent problems: 1) The modern military does not want high school drop outs. 2) Today's military does not take drug addicts or alcoholics. 3) The military has height, weight and other physical requirements that many immigrants cannot meet. 4) No criminals allowed. So how many of these immigrants will have a clean background check? 5) Age limits. I think 29-years-old is the maximum and I believe 17-years-old with parental permission is the minimum. So even more immigrants will be eliminated.
Basically all the above issues make my simple answer untenable. Alas, simplicity is the boilerplate of most plans. They just don't see the forest for the trees. Simple answers just aren't answers at all, but a way to justify stupid actions.
Political action by sound bites or bumper stickers, tweets, Facebook or other quick solutions are not solutions at all. So what do they represent? In my simple mind, simple answers represent more of a general philosophy than an actual game plan with step-by-step actions taken to achieve a specific goal.
I believe in God, but so do billions of other humans. The way we all behave proves there are millions of different ways to express this belief and just as many justifications for bad behavior or seeming beneficence.